3. arcsin (sin )

Q: 5. tanx = sin'x %3D tanx + cotx

A: We use Trigonometry identities to solve  Question 5

Q: 4. To integrate using trigonometric substitution the functio dx -2x we let x = sec 8 - 2

A: Given indefinite integral is ∫dxx2+2x We can solve by using the trigonometric substitution. Given…

Q: i) Sin 20easoal-Sin?

A: Use the trigonometric identities,…

Q: aresin(sin(-5). 3 arcsin( sin( – sin(-"#))- 4 arccos( cos(- 6. IT arccos( cOS 3 II

A:

Q: 4) Simplifying the Trigonometric ldentity tanx cosx

A: Explanation of the answer is as follows

Q: I--I---A sin dydx sin:

A: Given I=∫x=12∫y=xxsinπx2ydydx+∫x=24∫y=x2sinπx2ydydx In the given function variable y is in…

Q: Evaluating √9-x² dx using trigonometric substitution will lead to: -3

A:

Q: 4. у %3D sec^0 - tan'ө

A:

Q: Suppose that θ=arcsin(1/9). What is sin(2θ)? (round to 4 decimals)

A:

Q: 11.) cos os (sin-1 -tan-1%) 12.) tan (arccos %- arcsin (-12/13))

A:

Q: arc sin(3i/4)

A: We know that, Domain of sin-1x is -1≤x≤1.

Q: cos (arctan S (B) - arcsin (3)) - 5 5

A:

Q: 3) Find sin 0 if sec 0 : 8. and tan 0 < 0.

A:

Q: cos arcsin 12 %3D tan( aresin 12)) tan arcsin

A:

Q: 2. 1. sin (Arcsin ) 2

A: 1) Evaluate  sinsin-122

Q: 2. Explain why arcsin(sin(0)) = 0 but arcsin(sin(807)) # 807

A: Concept  arcsin(sin x) = x   is true  only when x lie in the interval [-π/2 , π/2]

Q: Find the smallest positive angle x in degree 1) cosx = -1/2 2) sinx = -1/2 3) tanx = -√3 4) Cscx =…

A:

Q: Suppose that θ=arcsin(2/5) in the first quadrant. What is sin(θ/2)? (round to 4 decimals)

A: Given : θ = arcsin(2/5) in the first quadrant.   To find : sin(θ/2)?

Q: Use the knowledge of the Mean Value Theorem to prove the trigonometric identity x – 1 arcsin 2…

A: In order to prove the identity, we need to consider a function and by using mean value theorem we…

Q: It is true that sin (3pi/2)=-1. Explain why arcsin (-1)≠(3pi/2)

A:

Q: Prove the identity  cscA-sinA = cotAcosA

A: Given,        cscA-sinA = cotAcosA

Q: lim, 20 sin5x.cot2x = ?

A:

Q: 5) Evaluate the given expression without the aid of a calculator tan[arcsin( +1 x+ 6 --)]

A: We have to evaluate the given expression without the aid of a calculator.

Q: arctan(−1)= arccsc(csc(5π/2))= sec−1(−tan(3π/4))= tan(cos−1(−7/12))= sec−1(−1)=…

A: arc tan(-x) =-arc tan(x) arc csc(csc(x)) =x Note : According to our guideline, we can solve first…

Q: 5. Establish the identity: tan 0 +cot 0 = sec 0 csc LHS COSE Sine Sude

A: consider the given identities

Q: cos-1 2. sin-(-1) 3. arcsin (-) 2 2.

A: Use the inverse identity, f-1(f(x))=x So,  sin-1sinx=x    where x∈-π2,π2cos-1cosx=x    where x∈0,π…

Q: Sine- -Cos zo

A: Using trignometric property

Q: Sin sec" 3. 2.

A: (1) We have to evaluated sinsec−1−23 Use he following identity  sinsec−1x=1−1x2

Q: Let Oses and let 3x = sece. Then sine is 2

A:

Q: 12.) tan (arccos %- arcsin (-12/13))

A:

Q: If  arcsin(x) = 1.25  then  arcsin(-x) = ?

A: It is given that, arcsin x=1.25 Take sine of both sides: sin arcsin x=sin 1.25 Result: sin arcsin…

Q: mode.) 1. y = arcsin(0.92837781) 2. y = cot-(-0.92170128) 3. y = arcsec(-4.7963825)

A: To calculate the following values

Q: arcsin (0.3)=

A:

Q: 14. Using the identities, find tanx and cscx if secx = 5 and sinx <0 %3D

A: Given that        Sec x = 5 and sin x &lt; 0 We have to find the value of tan x and csc x.

Q: 3. Find the area of one of the sine curve.

A:

Q: (sece +tane)(1+sine)de =

A: Evaluate ∫π6π4secθ+tanθ1+sinθdθ

Q: a tangent line to approximate the value of sin( + to three decimal places.

A: Let f(x)=sinx. We have to use the tangent line to approximate the value of sinπ4+1100. The formula…

Q: 7) Evaluate sin (arctan (arcsin (1))).

A: To evaluate the following.

Q: 22. What is the minimum amount of information that you must have in order to be able to apply the…

A: The minimum information that you must have in order to be able to apply the law of sines is: 1) Two…

Q: tan(cos−1(−7/12))= sec−1(−1)= tan(sin−1(−3/7))= arcsec(−√2)=

A:

Q: 10. y = arcsin 11. y = csc-1I

A:

Q: 2 sin (arcsin 0) = _____. -2 0 2 90

A: sin(sin-1x)=x  only when x∈ -π2, π2x=0 ∈  -π2, π2

Q: . What is the mathematical relationship between sine and cosecant, cosine and secant, and tangent…

A:

Q: 1- sine sece – tan 0 Cos e

A:

Q: Calculate arcsin 0, arcsin 1, arccos V3 arctan 1, arccot(V3) 2

A:

Q: TI tant@-2 tan Bzl show that 2cose - Cos"B2o

A:

Q: Cos cos arcsin 4. arctan 9

A:

Q: 8. If tan 0 = 15 what is sin 0? sin 0 = %3D iblo

A: The solution is given below in the next step:

Q: Sin(arctan(1/2)-arcsin(1/2))=

A: tan-1x=sin-1xx2+1

Q: arcsin(2x) ·

A:

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.